The Rockets had escaped so often, had made the most of so many last chances, as Chase Budinger rose for the 3-pointer that would have won the game, there was every reason to believe it would fall.

They needed Dirk Nowitzki to miss a free throw at the end of regulation and got it.

They needed Chandler Parsons to drill a 3-pointer off the dribble to force overtime. He hit it.

They even needed to trap the Mavericks in the backcourt with the game down to its final overtime seconds, and they did it.

Finally, they had brought the game to the same sort of corner 3 that had beaten the Thunder and stunned the Lakers.

But after all the Rockets had made happen to push the game to a final shot, Budinger’s 3-pointer and the Rockets came up short, with Dallas holding on for a 101-99 overtime win Saturday night at Toyota Center that dropped them out of the Western Conference’s top eight teams.

“We played hard. We definitely had effort. And we definitely put ourselves in a position to win the game,” said Parsons, who had 12 points, 11 rebounds and six assists, getting his first two career double-doubles in consecutive games. “Things didn’t really go our way.

“It was a tough game. They played well, but we deserved to win that game.”

They had their final last chance after the ball did bounce their way, with Goran Dragic’s pass to Budinger slapped away, before Dragic recovered to get it to Budinger in the corner.

Like it was drawn

“The play worked for us,” Budinger said. “We got Goran the ball on the move. He turned the corner and attacked the basket. What he does so well, when he attacks the basket, he draws so many people. He was able to find me in the corner. Unfortunately, I just missed the shot.”

Dallas forward Shawn Marion had left Budinger to help cut off Dragic’s drive, getting his hands on Dragic’s bounce pass to the corner.

But Dragic redirected it to Budinger for just enough time to shoot for the win before the buzzer.

“It threw off the rhythm a little bit,” Budinger said, “but I can’t make any excuses because I still got a good look at it.”

The Rockets lamented many other good looks that missed long before the last one. Dragic had put the Rockets in front with a 3-pointer with 3½ minutes remaining in regulation, finishing a 9-2 run, but the Rockets made just one of their next six shots. Marcus Camby had come in to shut down Nowitzki down the stretch, but Jason Terry and Brandan Wright put the Mavericks in front 90-86 with 19.4 seconds left.

“We were up by three and had two or three really good looks,” Rockets coach Kevin McHale said. “We didn’t knock them down. I thought any of those probably would have had the game going in our direction.”

Never say die

The Rockets got out of that hole when Camby tipped in a miss and Nowitzki missed a free throw. Parsons line-drived in his 3-pointer with 3.3 seconds left to tie the game. The game headed to overtime when Courtney Lee slapped away an alley-oop for Wright and Terry missed at the buzzer.

The Rockets were in as much trouble in overtime. With the game tied at 97, with 90 seconds left after Lee’s jumper with just the tip of his shoe on the 3-point line, Dragic was called for an offensive foul on a drive to the rim. Terry put the Mavericks in front, and after Wright blocked a Lee jumper — giving him a career-high seven and the Mavericks 15, the most against the Rockets since 1991 — Lee fouled Nowitzki with 18.5 seconds left.

Lee said he never touched Nowitzki and Nowitzki agreed, but even after Nowitzki made both free throws, giving him 31 points and the Mavericks a four-point lead with 18.5 seconds left, the Rockets again rallied. Dragic put in a reverse before he and Parsons trapped Roddy Beaubois in the backcourt for an 8-seconds violation with 6 seconds left.

McHale’s praise

That was enough time for the Rockets to get the shot they wanted, only to watch it bounce off the side of the rim and away.

“We kept on battling back,” McHale said. “I was proud of the guys for doing that. We have to keep fighting. It was just hard to lose that game because the guys played so hard. You want them to have that good feeling.”